The Wheeler–DeWitt equation (REF ) has been studied intensively since 30 years [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}. In fact, this is an equation on superspace [31]}, defined as a space of all equivalence class of metrics related by the action of the diffeomorphism group of a compact, connected, orientable, Hausdorff, \(C^\infty \)  3-dimensional spacelike manifold without boundary \(\partial M\) . If \(Riem(\partial M)\)  consists all \(C^\infty \)  Riemannian metrics on \(\partial M\) , and \(Dif\!f(\partial M)\)  is a group of all \(C^\infty \)  diffeomorphisms of \(\partial M\)  that preserve orientation, then the Wheeler superspace \(S(\partial M)\)  is the space of all orbits of \(Dif\!f(\partial M)\) , i.e. \(S(\partial M)=Riem(\partial M)/Dif\!f(\partial M)\) . \(S(\partial M)\)  is a connected, second-countable, metrizeable space. All geometries with the same kind of symmetry are manifold in \(S(\partial M)\)  - they have homeomorphic neighbouhoods. However, symmetric geometries neighbourhoods are not homeomorphic to nonsymmetric geometries ones, and by this \(S(\partial M)\)  is not manifold. Superspace can be decomposed by its subspaces on a countable, partially-ordered, \(C^\infty \) -Fr\(\mathrm {\acute{e}}\) chet manifold partition, that is an inverted stratification indexed by the symmetry type - geometries with a given symmetry are completely contained within the boundary of less symmetric geometries. The minisuperspace models, i.e. Quantum Cosmology [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}, study certain strata of superspace. Fischer [31]} proved by suitable choice of a subgroup of \(Dif\!f(\partial M)\)  and by action of this subgroup on \(Riem(\partial M)\) , for n-dimensional \(\partial M\)  the superspace \(S(\partial M)\)  can be extended to a manifold \(S_e(\partial M)\)  such that \(\dim S_e(\partial M)/S(\partial M)=n(n+1)\) .
